{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x9c2d8d0>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MS+xKqYbAJ8Aftda5Fz+utZ6ltU7SWidFRnrHFWHBAX68dGMix/IKmbZwh9XhCGELuQXF/OmjLcSGh/D4iM5Wh+OWTEnsSil/ypP6B1rrT83Yp130bN2Eey9rz6cbM/h6+1GrwxHC4/194U6O5pzjxRsTCQ7wszoct2RGV4wCZgMpWuuXHA/Jfu67oiPdW4bx2KfbyMorsDocITzW19sz+WTjYe69vAO9WjexOhy3ZcaMfQAwCRiilNpc8WeECfu1DX9fH/41PpGzRaU8+sk2ueOSEAZk5RXw+IJtdGvZiPuv6Gh1OG7NjK6Y1VprpbVO0Fr3qPiz2Izg7KRDs1AeuSqe71KzmLv+kNXhCOFRtNY89sk28gtL+NeNPfD3lWsrayKj40K39I9lQIdwnvpyJwdOyEJhQtTVvPWH+DY1i0euiqdj81Crw3F7kthdyMdH8fy4RHx9FA/N3yJrtwtRBwdPnOWpL3fSv304t/aPtTocjyCJ3cVaNG7Ak2O6knzgFDNXykJhQtSktEwzdf5mfJTi+RsSZYGvOpLEboGxPVpydbco/rV0NzuOyEJhQlRn1sp0kg+cYtrorrRsLAt81ZUkdgsopXjm2u6ENQhg6rwtslCYEFXYeSSXl5bu4qquUVzXy+tXKakXSewWaRoSwPRx3dl1LI8Xl8hCYUJUVlBcytT5mwlrEMA/rusuC3zVkyR2Cw2Jb87v+rbmv6v28c2OTKvDEcItaK356+fbSc3MY/q47jQNkQW+6ksSu8X+MqoLiTFhPDR/C3uz8q0ORwjLfbjuIPOTD3PfkA4MiW9udTgeSRK7xYL8fXljYm8C/Xy46/1k8gtLrA5JCMtsPHiKaQt3MDgukj8OjbM6HI8lid0NtGjcgNdu6sm+42f40/wtsuSA8ErZeYXcM2cDUWFBvDKhB77S2miYJHY30b99BI9d3Zmvd2Tyxgrpbxfepbi0jHs/3EjOuWJmTkySG2c4SBK7G7l9UFtGJUTzwje7WLnbO25GIgTAs4tTWbfvJP+8LoEuLRpZHY7Hk8TuRpRSTB+XQMdmodw/dxOHTp61OiQhnO7zzRm89cM+bh0Qy9ie0q9uBknsbiY4wI8Zk3pTWqa5e84GuXhJ2NrOI7k88slW+sQ2lbshmUgSuxtqGxHCy+N7sONILo8vkPXbhT2dPlvEXXOSCWvgz79/11OW4jWRjKSbuqJzc/44tCOfbszg/TUHrA5HCFOVlmkemLuZzJwC3pjYm2ahQVaHZCuS2N3Y/UM6ckV8M578YifJ+09aHY4Qpnll2W5W7M5m2uiucos7J5DE7sZ8fBQvje9BTJMG3PPBRrJy5X6pwvMt2ZHJq9/t5cakGG7q09rqcGxJErubC2vgz8xJSeQXlHDPBxspKimzOiQhDEvLzmfq/C0kxITx5JhusriXk0hi9wCdokKZPi6BDQdO8fSinVaHI4Qh+YUl3P3+BgL8fHhjYm+C/H2tDsm2/KwOQNTNNYkt2Hr4NP9dtY+EmMaM6x1jdUhC1JnWmoc/3kJadj5zpvSVm2Y4mczYPcgjV8Vzabtwnliwje0Zcucl4TlmrUxn8bZMHr06nv4dIqwOx/YksXsQP18f/n1TT8JDArjr/Q1yMlV4hOW7snju61RGJkRzx6B2VofjFSSxe5jwhoHMmNSbU2eLuPmtdeScK7Y6JCGqteHAKe6Zs5HO0Y2Yfn2CnCx1EUnsHighpjEzJ/UmLTuf299dz7kiWXZAuJ9dmXnc9s56osKCePe2PoQEyik9V5HE7qEGdYzk5fE9ST5wins/3EhxqbRBCvdx6ORZJs1eS5C/D+/d1oeIhoFWh+RVJLF7sJEJ0Tw9thvfpWbx8MdbKSuTNWWE9bLzCpk0ey2FJWW8P6UvrZoGWx2S15HfjTzc7/q24dSZIl5YspuwBv787ZouUscUlsktKGbyW+s4llvIB3f0Ja55qNUheSVJ7DZw7+UdOHmmmLd+2Ed4SAD3XdHR6pCEFyooLuX2d5PZk5XHm5MvkTVgLCSJ3QaUUvzfyM6cPlvEi0t30zgkgEn92lgdlvAiJaVl/OHDjazff5JXJvRkcFyk1SF5NVNq7Eqpt5RSWUqp7WbsT9Sfj4/iuXEJXBHfjL9+vp0vthyxOiThJcrKNI98so1lKVk8OaYboxNbWB2S1zNrxv4O8G/gPZP2Z7nirCwypj5EzL9ewi+ybrMPI9uYyd/Xh//8rhc3z17H1PmbadTAX2ZOlYxbOI7EZoncnXA3kcGRnMkpJHnRPjLTcxn/f31M28abaK15ZnEKn2w8zNRhcdb9pvh8RziT9et/D2kGf95j3jYewpTErrVeqZSKNWNfZjOabI+//gbnNmwg+z+vEz3tb07bxuwPgyB/X/47OYkJs9Zw9/sb+OCOvrasdRpJuLtO7SI9J50lO79jbM7tBKe1AA1lpdV3ExnZxps+DF5fnsbs1fu4pX8s9w3pYM5OjSTcqp5f078b3cZDPgxsX2Ovb7JNTeyBLiz8+fvTc+dyeu5cVGAg8Vs2m7aN0fjqIqyBP+/edgk3zPiJW99ez0d3X2q77gQjCTe4qBG9Dg8nPqsP4ENZHW45aGQbI7F5og/XHuT5b3YxtkcL/jrKxG4sIwnXVdw5tkpc1seulLpTKZWslErOzs52+vFSE3uQEt+Z03PngtacnjuXlPjOpCb2qHG79kuX0GjUSFRQ+a26VFAQja4ZRYdlS03dxmh8ddUsNIg5U/oS6OfDpNlrOXTyrCn7dRfBRY3ou3cs49Y/gt/uSMpKdK2Jc+juyXQ91h8/HYCfrtucxsg2RmLzNIu3HeWJz7YxJL4Zz9+QiI+PtNi6E5cldq31LK11ktY6KdJgyaE4K4v9EydRUocPBiPJFsC/WTN8GjZEFxaiAgPRhYX4hDSssUxiZBuj8UHdx6FV02Dem9KHc0WlTJq9luy8whqfb4VxC8fx1JqnyD5b/rOcySlkxYepzHt6XY3bGUm4S+PeYUfzHyjxKaJElThtGyOxGR0HK6zak80DczfRu3UT/nNTr+pvQv18R5gW9us/z3thO66Lx8KjSjH1KVsYSbbnlRw/QeMJE2gy/kZOzZtfpw+S+m7jSHz1GYf4qEa8fesl/O7NtUx+ax3/u7MfYQ38az2GqxgtWyyNe4feh4cTn90XtE+dEui5gDzWdvic7W2+Z2zOHQSmt0CX1XwsI9sYic1TyjebDp7irvc30D6yIbNvuYQGATXcLMNDyhYu4eKxMCWxK6X+B1wGRCilDgN/01rPNmPfYLyGbSRBA7T692s/fx39t786bZv6xmd0HHq3acobE3tz53vJjJ/5E+/e1ofmjdzjrvBGathgLOF2atKJHs16cHfi3UQ0iCg/qbl4P5lp1a9tb2QbI7EZHQdXWrUnm7ve30BEw0Deu62PW00QCGlW/UlNM7fxEGZ1xfzWjP1Up/3SJWRNn07esm/RBQWooCBChw2l+cMP17idkWTrSvWNz+g4AFzeqRlvj25L5p/+zC0np/Dv+4bRPrKhQ/FfzEg3yNDdk4nOa4eqZ1XQSML9ePTHF3wfEhbI4N92qvE4RrYxEpvRcXBVB07Bs+0YVHiCnT7AWeCligec0Q1iJOEaicHINh7yYeARpRhHyhZ24ug4tP9qPk2PpzNi0yLGvRHC27f2oUerxqbFZ6ScYKRsAcYSrqsYic3oOLiihPPmqnRuLzxR9YPOKCW4Udvgr7hzbJV4RGIH42UVuzEyDpVLOAoYuucHhu75gaK5fny/4Fsu72TObMNIOcFI2cKOjI6DM0s4Wmv++XUqM1ekc7t7VO5EHXlMYnf3soqrGBmHqko4/pcNYVrzy9nwbjLPXZ/A9SbcHNtIOcFI2cKOjI6D0RJObYpLy3jkk618ujGDif1aQ82XY1TNQ8oWLuHisfCYxC6Mq6qEE9y4EW8+OJw739vAQx9t4cSZQu78TfuftzFSuzVSTnDnkoorGR0HI2Ne2//t2aISfv/BRpbvymbqsLjyK0qNJHYPKVu4hIvHQhK7l6iqhBMa5M87t13C1Plb+MfiVLJyC3l8RGd8fNTPtds165Yxcd0ITje+BLQyvTVQOMbImO86tYv0E6ks2bKYsfuvIPjUAMCHMvw5eaaI295Zz9bDp/nHtd25qW9r1/0wwjSS2L1EdSWcQD9fXpvQk4iQAN5cvY/j+YVMH5f4c+22a2YfTgUrdAlAzQlayiquZ2TML6zLK8r4pW1x3IwfyTh1jjcm9mZ416hfNpKyikdR2oJ+2aSkJJ2cnOzy44rqaa15fXkaz3+zi0EdI7hy6WZyw9qD+nXt9t4ZQyyIUJjliT/PqrYuPzOqmDcnX0Kftk0tiEzURim1QWudVNvz5J6nAii/Wce9l3fgueu788Pe47zX7x3UudX4lBahyoqtDk+Y6MJlEi78v/3o7v6S1G1AEru4wPhLWjNzUhKZTfIpLvqIvmv/RvSxNfiUFuFDmdXhCROcC8hjbexHfJw4jZLGK/GlEB/KE3ynKHutAuqtpMbuBerb4TKsS3Na7+xAWG42P7TtwGVTR9Lj26XszI4kv2VCrcez+oYjXsXA+uCdCovoUVjI3acziAhM4UzkHJLzbyCzOB6ouszmTWvM24Ekdi9g5OrEReMWsHtQHre8tY5Xl2TxyFXjuW1A2zotz+qMNeZFNQwsLjU/pxSfM6d+/j7E9zSDw/5bcSL09iq38ZRFykQ5SexewOjViXHNQ1l0/yAe/mQrTy9KYdWe47xwQyKRoYFVPt+RG44I10jef5IHSmdxrKiAqVfGcddv2uNbhw9rT1ikTPxCauxewMj64Oc1CQlg1qTePDWmK2vST3D1K6tYsbvqZQwcWWNeOFdpmeaVZXu4ceZP+PooPr6nP7+/rEOdkjo49hoSrieJ3QsYuVlEZUopJl0ay8I/DKRpiD+T31rH01/upLCk9ILnyWJt7inj9Dl+O2sN/1q2m9GJLVh0/8B6L/7m6GtIuJYkdi9w/urEj5P+SUlcNr7+Ch/f+t/KrFNUKAv/MJCJ/Vrz5up9XP/Gj6Rn51/wnPNXuMbOm0vjCRMoOX7crB9DGPDVtqNc/fJKdhzJ4aUbE3l5Qk9Cg+q/jrpZryHhGvI7lQcx2plg5hWhQf6+PD22O4M6RvLIJ1sZ9dpqpo3uyg29Y1BKGV6szes7aQx0t/z8eBXb6ZBmPP7pVv637hCJMWG8MqEnsREhhsMz8hqSThrryJWnHqT7u93x9/EnpDjsV50JVlwNejTnHA/O28ya9JOMSojmmWu7G76rztFpf+f0vHk0Hj/eOztppoXV8Fj9PoB3Hsnl/rmb2JuVz12D2/HQsE4E+Ln+l3N3e73aQV2vPJUZuwdxt86E6LAGfHB7P2asSOOlpbvZdPA0r/62B73b1P3KRemkMY/Wmnd+3M+zi1MJC/ZnzpS+DOwYYVk87vZ69SZSY/cg7tiZ4OtTvhTBR3dfio8P3DhzDa9+u4fSsrq9iaWTxhwn8guZ8m4yf/9iJwM7RvD1A4MsTergnq9XbyGJ3YO4c2dCr9ZNWHT/IEZ2j+alpbu5/o0fWb//ZK3bSSeNY0pKy/hw7UGGv7yK1XuPM+2aLsyenER4w6qvNXAld3692p0kdg/i7p0JjYL8eWVCD/41PpEjp89xw4yfuP3dZPZm5dW4nXTS1J/Wmm92ZDL85ZU8vmAbbcKD+ez3A7hlQFuUco/XhLu/Xu1Mfj+yiJGOAU9Y71wpxbU9YxjeNYq3Vu9jxop0rvzXSm5MasWDw+Jo3ujXN8905LaHbtlNY6TDpR7rnSfvP8mzX6Wy4cAp2kWGMHNSb67s0txtEvp5Rl+v0k3jOOmKsYi3dAycPFPEa9/tYc6aA/j6KKYMbMtdg9vTyEAvdVXcspvGxA6XyvZm5fHc17tYuvMYkaGBPDg0jhuTYvDztdcv3t7y3jBCumLcnLd0DDQNCeBv13Tl1v5teWHJLv7zfRofrj3IH4Z0ZGK/1gT6+Rrarzd10xzLLeDlZbuZt/4QwQF+PDQsjimD2hIcYM+3r7e8N5zJnq8MD+Csu8u7q9bhwbz6257cMagd//w6hae+3Mk7P+7jT1d24pqEFnVaNbKy9kuXkDV9OnnLvkUXFKDiXbwXAAANiUlEQVSCgggdNpTmDz/spJ/A9fIKipm5Ip03V6dTWqa5+dJY7hvSwS1OjDqTt703nEFGziLe2jHQPSaMOVP68u5tfWgY6M8Dczcz+j+rWb2nfidM7dxNU1RSxts/7GPw88v59/d7GdYlimVTBzNtdFfbJ3Xw3veGmWTGbhEjd5e3C6UUg+MiGdQhgs82Z/Dikt1MnL2W/u3DGX9JK67sEkWDgNpLNOe7aZqMv5FT8+ZTkl31qpOeIjOngM83Z/DB2oMcPHmW/u3DefTqeBJi6rdgl6fz5veGWSSxW8QTOlyczcdHcV2vGEZ0j2bOmgPMXr2PB+ZuJiTAl6u6RXNdr5b0axde7dKyjnTTOFU9OlzyC0v4ensmCzYd5se0E2gNPVs35skxXRkcF+l2nS6uIO8Nx0lXjAmkPcscZWWaNftO8NmmDBZvyyS/sISoRkGM6dGCa3u1JD6qkSnHqVeLpNHFuWpQUlrGqr3HWbAxgyU7MykoLqN102DG9mzJ2B4taBfZ0NB+vZm3vAelK8aF5LZh5vDxUfRvH0H/9hE8OaYbS3ce47NNGcxevY+ZK9OJjwrlul4tGZ3YkqiwX/fD11W9bt1n4NZzVdFasy0jhwWbMvhiyxGO5xcR1sCf63vFcF2vlvRq3cQrZ+dmkffghSSxm0Das8wX5O/LNYktuCaxBSfyC/ly61E+3ZTBPxan8uxXqQxoH8G1PVsyvFsUDQPr9jK2okXy0MmzfL45gwWbMkjLPkOArw9D4ptxba+WXNYp0nC7p7iQvAcvZEpiV0pdBbwC+AJvaq3/acZ+PYW0ZzlXeMNAJvePZXL/WNKz8/lsUwYLNmfw0EdbeGzBNjpHhRIf1Yj46FA6RzciPiqUxsEBv9qPM1sktdZknD5H6tE8Uo7mkpqZR0pmLunZZwDoE9uUKQPbMbJ7NGHB5lycJX4h78ELOZzYlVK+wH+AYcBhYL1SaqHWeqej+/YUS+Peoffh4cRn9wXtIyvZOVG7yIZMvbITDw6LY8OBU3yzI5OdR3NZmnKMecmHfn5edFjQz0k+ProRXaJDiQ2PMLVF8sO1B0nNzC1P5pm55BX80prXJjyY+KhQxvWO4ZqEFrRqGuzwzy6qJ+/BC5nx0/cB9mqt0wGUUnOBMYDXJHZpz3I9pRRJsU1Jii1f+11rTXZeISmZeaQezf151rxydzYlFUsIB/j58PTG3fgmDeXQwOG0X7OUoO3pzPpiR7XHqakC//iCbTQM9CM+KpQxPVpUfJA0olNUaJ3LQ8Ic8h68kBmvvpbAoUrfHwb6XvwkpdSdwJ0ArVu3NuGw7kPas6ynlKJZoyCaNQpicNwvM/CikjL2ZuWXz6wz8/ii7QPsyszj3NFSaHN1+ZM2HK52v/cSRgS//n8sDIxg1f2XE9OkgZz0dAPyHryQw+2OSqkbgOFa69srvp8E9NFa31fdNu7c7ugtbVNeyYHWRbdcRVI4xBPf665sdzwMtKr0fQxwxIT9WkLapmzMgdbFerVICo9g5/e6GYl9PdBRKdUWyAAmADeZsF9LSNuUqMybVpH0NnZ+rzvcG6S1LgH+AHwDpADztdbVn41yc3KfRlGZ3JPVvuz8Xjel6VNrvVhrHae1bq+1fsaMfVpFVpYTldl5FUlvZ+f3unTzX0Tu0yguJvdktSc7v9ft9ftHJUbPeEvblI3VY9XFytx2FUnhECPvdU/ppLHt6o5y30Sbc8Kqi2aTFkn7sTqveP3qjnY+4y0wbdVFZ5IWSfvxlLxi28QuiwIJq0iLpH15Sl5x7+gcYOcz3sK9SYukfXlKXrFtYrfzGW/h3qRF0r48Ja/YthQj3S3CSna70bYo5yl5xSO6YjylxUgYYLS7xQO6YoyQThp7MiuH2aorxs6L9Xg9o90tHpy8ayKdNPbk6hzmEYndU1qMhDBKOmnszdU5zCNOntp5sR4hQDpp7M7VOcwjEruntBgJYZR00tibq3OYRyR2T2kxEsIRstiYfbk6h3lEXcNTWoy8npFOFYMLc9mRI4uNSTeNe3N1DvOIdkfhIaaF1fCYfAg709Fpf+f0vHk0Hj9eumlszFbtjkKIqkk3jaiKR9TYhRBVk24aURVJ7EJ4MOmmEVWRUoyomk0v2bcjo+vSyAlX+5LELqpm5FJ/6XCxhNFuGlm+wL4ksQvzyEzeI8gJV/uTGrsQXkZOuNqfJHYhvIyccLU/KcV4AzkRKi4iJ1ztTRK7N5AToeIicsLV3iSxi6rJTF5UIidcPYtnJHYpJZSTcRAWab90CVnTp5O37Ft0QQEqKIjQYUNp/vDDtW4r5ZtfuGosPOPkqdHbp9mNjIOwiCMnXCuXb7ydq8bCM2bsQgjL1feEq5RvfuHqsXAosSulbgCmAZ2BPlpr91mL193LFq6MT06EChPU94SrI+UbcO8STn1jc3Qs6svRGft24DpgpgmxmMto2cJIwjWyjSvLKu7wQSa8jqP98kY6cIx8GBjZpr6xufraAYdq7FrrFK31LrOCcQtGEq7UvoWokpHb/aUm9iAlvjOn584FrTk9dy4p8Z1JTexR67ZGatj12caR2Fx560PPqLFLKaGcjIPwMEb65Y2ULYzUsI1s40hJxZFbH9ZXrYldKbUMiKrioSe01p/X9UBKqTuBOwFat25d5wABKSWcJ+MgvICRsoWRhGtkG09ZjqHWxK61HmrGgbTWs4BZUH7PUzP2KYSwp/p24BhJuEaTtNHlGFzJM0oxRrh72cLd4xPCQkbKFkYSrpFtXFlSMUppbXzyrJS6FngNiAROA5u11sNr2y4pKUknJ7tPZ+QFXNUVI4QQ9aSU2qC1Tqr1eY4kdqPcOrELIYSbqmti94wlBYQQQtSZJHYhhLAZSexCCGEzktiFEMJmJLELIYTNWNIVo5TKBg4Y3DwCcN4iC8ZJXPUjcdWPxFU/7hoXOBZbG611rZe5WpLYHaGUSq5Lu4+rSVz1I3HVj8RVP+4aF7gmNinFCCGEzUhiF0IIm/HExD7L6gCqIXHVj8RVPxJX/bhrXOCC2Dyuxi6EEKJmnjhjF0IIUQO3T+xKqeeVUqlKqa1KqQVKqcbVPO8qpdQupdRepdSjLojrBqXUDqVUmVKq2jPcSqn9SqltSqnNSimnr3xWj7hcPV5NlVJLlVJ7Kv5uUs3zSivGarNSaqET46nx51dKBSql5lU8vlYpFeusWOoZ1y1KqexKY3S7i+J6SymVpZTaXs3jSin1akXcW5VSvdwkrsuUUjmVxsvp6+wqpVoppb5XSqVUvBcfqOI5zh0vrbVb/wGuBPwqvn4OeK6K5/gCaUA7IADYAnRxclydgU7AciCphuftByJcOF61xmXReE0HHq34+tGq/h8rHst3wRjV+vMDvwdmVHw9AZjnJnHdAvzbVa+nSsf9DdAL2F7N4yOArwAF9APWuklclwFfunisooFeFV+HArur+H906ni5/Yxda71Ea11S8e0aIKaKp/UB9mqt07XWRcBcYIyT43LLG3nXMS6Xj1fF/t+t+PpdYKyTj1eTuvz8leP9GLhCKaXcIC5LaK1XAidreMoY4D1dbg3QWCkV7QZxuZzW+qjWemPF13lACtDyoqc5dbzcPrFf5DbKP+Uu1hI4VOn7w/x6IK2igSVKqQ0V9311B1aMV3Ot9VEof+ED1d0qKkgplayUWqOUclbyr8vP//NzKiYWOUC4k+KpT1wA11f8+v6xUqqVk2OqK3d+D16qlNqilPpKKdXVlQeuKOH1BNZe9JBTx8stbo1XlxtmK6WeAEqAD6raRRX/5nC7j0k38h6gtT6ilGoGLFVKpVbMMqyMy+XjVY/dtK4Yr3bAd0qpbVrrNEdju0hdfn6njFEt6nLML4D/aa0LlVJ3U/5bxRAnx1UXVoxXXWyk/DL8fKXUCOAzoKMrDqyUagh8AvxRa5178cNVbGLaeLlFYte13DBbKTUZGAVcoSsKVBc5DFSeucQAR5wdVx33caTi7yyl1ALKf912KLGbEJfLx0spdUwpFa21PlrxK2cV9xK8YLzSlVLLKZ/tmJ3Y6/Lzn3/OYaWUHxCG83/lrzUurfWJSt/+l/LzTu7AKa8pR1VOqFrrxUqp15VSEVprp64jo5Typzypf6C1/rSKpzh1vNy+FKOUugp4BBittT5bzdPWAx2VUm2VUgGUn+xyWkdFXSmlQpRSoee/pvxEcJVn713MivFaCEyu+Hoy8KvfLJRSTZRSgRVfRwADgJ1OiKUuP3/leMcB31UzqXBpXBfVYUdTXr91BwuBmyu6PfoBOedLb1ZSSkWdPzeilOpDec47UfNWDh9TAbOBFK31S9U8zbnj5cqzxQbPMO+lvBa1ueLP+U6FFsDii84y76Z8dveEC+K6lvJP3ULgGPDNxXFR3t2wpeLPDneJy6LxCge+BfZU/N204t+TgDcrvu4PbKsYr23AFCfG86ufH3iS8gkEQBDwUcXrbx3QztljVMe4nq14LW0BvgfiXRTX/4CjQHHF62sKcDdwd8XjCvhPRdzbqKFTzMVx/aHSeK0B+rsgpoGUl1W2VspbI1w5XnLlqRBC2Izbl2KEEELUjyR2IYSwGUnsQghhM5LYhRDCZiSxCyGEzUhiF0IIm5HELoQQNiOJXQghbOb/ATXrUN/W00SsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=linspace(-2, 2, 24)\n",
    "y = x**2\n",
    "plot(x, y)\n",
    "plot(x, sin(x),'s')\n",
    "plot(x, cos(x), '>')\n",
    "plot(x, -sin(x), '*')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.        , -1.82608696, -1.65217391, -1.47826087, -1.30434783,\n",
       "       -1.13043478, -0.95652174, -0.7826087 , -0.60869565, -0.43478261,\n",
       "       -0.26086957, -0.08695652,  0.08695652,  0.26086957,  0.43478261,\n",
       "        0.60869565,  0.7826087 ,  0.95652174,  1.13043478,  1.30434783,\n",
       "        1.47826087,  1.65217391,  1.82608696,  2.        ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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   "language": "python",
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  "language_info": {
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